The SNR in (REF ) is equal to that in \( M \) -antennas systems with path-loss \(c_k\delta \varepsilon _{k}\) . Besides, the SNR is uncorrelated with \(\tau \)  and the same SNR can be realized by applying the corresponding power scaling in perfect CSI-based systems[1]}.
In other words, the increase of \(N\)  could compensate the detrimental effects of limited pilot lengths, and \(\tau =1\)  is adequate in (REF ).
Furthermore, it is easy to find that the rate is an increasing function of Rician factors \(\delta \)  and \(\varepsilon _{k}\) . Therefore, the LoS environment is beneficial for RIS-aided single-user systems.
